Relaxation-time distribution functions and the kramers-kronig relations

Physica ◽  
1954 ◽  
Vol 20 (7-12) ◽  
pp. 1266-1270 ◽  
Author(s):  
Malcolm K. Brachman ◽  
J. Ross Macdonald
Keyword(s):  
Relaxation Time ◽  
Time Distribution ◽  
Distribution Functions ◽  
Relaxation Time Distribution

The relaxation time distribution in dielectrics

1992 ◽  
Vol 11 (14) ◽  
pp. 988-990 ◽  
Author(s):  
S. N. Al-Refaie ◽  
H. S. B. Elayyan
Keyword(s):  
Relaxation Time ◽  
Time Distribution ◽  
Relaxation Time Distribution

A laboratory study of NMR relaxation times in unconsolidated heterogeneous sediments

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. G73-G83 ◽  
Author(s):  
Elliot Grunewald ◽  
Rosemary Knight
Keyword(s):  
Grain Size ◽  
Relaxation Time ◽  
Time Distribution ◽  
Relaxation Times ◽  
Nmr Relaxation ◽  
Unconsolidated Sediments ◽  
Relaxation Response ◽  
Relaxation Time Distribution ◽  
Near Surface ◽  
Heterogeneous Sediments

Nuclear magnetic resonance (NMR) relaxation-time measurements can provide critical information about the physiochemical properties of water-saturated media and are used often to characterize geologic materials. In unconsolidated sediments, the link between measured relaxation times and pore-scale properties can be complicated when diffusing water molecules couple the relaxation response of heterogeneous regions within a well-connected pore space. Controlled laboratory experiments have allowed us to investigate what factors control the extent of diffusional coupling in unconsolidated sediments and what information is conveyed by the relaxation-time distribution under varied conditions. A range of sediment samples exhibiting heterogeneity in the form of a bimodal mineralogy of quartz and hematite were mixed with varied mineral concentration and grain size. NMR relaxation measurements and geometric analysis of these mixtures demonstrate the importance of two critical length scales controlling the relaxation response: the diffusion length ℓD, describing the distance a water molecule diffuses during the NMR measurement, and the separation length ℓS, describing the scale at which heterogeneity occurs. For the condition of ℓS > ℓD, which prevails for samples with low hematite concentrations and coarser grain size, coupling is weak and the bimodal relaxation-time distribution independently reflects the relaxation properties of the two mineral constituents in the heterogeneous mixtures. For the condition of ℓS < ℓD, which prevails at higher hematite concentrations and finer grain size, the relaxation-time distribution no longer reflects the presence of a bimodal mineralogy but instead conveys a more complex averaging of the heterogeneous relaxation environments. This study has shown the potential extent and influence of diffusional coupling in unconsolidated heterogeneous sediments, and can serve to inform the interpretation of NMR measurements in near-surface environments where unconsolidated sediments are commonly encountered.

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